Related papers: Complexity of Ising Polynomials
We prove some variants of the exponential formula and apply them to the multivariate Tutte polynomials (also known as Potts-model partition functions) of graphs. We also prove some further identities for the multivariate Tutte polynomial,…
We analyze Ising/Curie-Weiss models on the Erd\H{o}s-R\'enyi graph with $N$ vertices and edge probability $p=p(N)$ that were introduced by Bovier and Gayrard [J.\ Statist.\ Phys., 72(3-4):643--664, 1993] and investigated in two previous…
Finite-dimensional representations of Onsager's algebra are characterized by the zeros of truncation polynomials. The Z_N-chiral Potts quantum chain hamiltonians (of which the Ising chain hamiltonian is the N=2 case) are the main known…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
We initiate a study of the classification of approximation complexity of the eight-vertex model defined over 4-regular graphs. The eight-vertex model, together with its special case the six-vertex model, is one of the most extensively…
The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate…
In this paper we analytically study the recurrence equations of an Ising model with three competing interactions on a Cayley tree of order three. We exactly describe paramagnetic and ferromagnetic phases of the Ising model. We obtain some…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
We present a comprehensive numerical study of dynamic phase transitions in the two-dimensional kinetic Ising model under a non-antisymmetric time-dependent magnetic field including a sinusoidal term and a second harmonic component. We…
Isoradial dimer models were introduced in \cite{Kenyon3} - they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of…
The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in…
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…
We study random plane partitions with respect to volume measures with periodic weights of arbitrarily high period. We show that near the vertical boundary the system develops up to as many turning points as the period of the weights, and…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
The 3D one-component spin system in an external magnetic field is studied using the collective variables method. The integration of the partition function of the system over the phase space layers is performed in the approximation of the…
The Ising model is well-known for illustrating the fundamental characteristics of phase transitions in closed systems. In this article, we propose a generalization of the two-dimensional Ising model to open systems, considering the…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…